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1st Grade Math
Practice Test 7 for 1st Grade Math: real questions and explanations from the Varsity Tutors practice-test pool.
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What is 45−10?
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What is 45−10?
Explanation: This question tests 1st grade ability to mentally find 10 more or 10 less than a two-digit number (CCSS.1.NBT.C.5). To add or subtract 10 mentally, use place value understanding: since 10 equals 1 ten and 0 ones, subtracting 10 means removing 1 ten (tens digit decreases by 1), while the ones digit stays the same. For example, 45 - 10 = 35 because 4 tens - 1 ten = 3 tens, and the 5 ones remain unchanged. The scenario involves finding 45 - 10 mentally, with a hint that only the tens digit changes. Choice C is correct because subtracting 10 from 45 means removing 1 ten: 4 tens - 1 ten = 3 tens, ones stay 5, giving 35. Choice A is a common error where students add 10 instead of subtracting, resulting in 55; this happens because they reverse the operation, perhaps misreading the subtraction sign. To help students: Use base-10 blocks to show physically removing 1 ten-rod while ones stay constant; practice on hundred charts (subtract 10 = up one row); emphasize pattern 'tens change by 1, ones stay same'; provide many examples showing ones digit constant; connect to skip counting by 10s; use number lines with jumps of 10; practice mental math daily with quick '10 less' questions; explain why this is efficient compared to counting by ones; make the place value connection explicit.
Subtract 11−6 by finding the missing addend: 6+?=11.
Explanation: This question tests 1st grade understanding of subtraction as an unknown-addend problem (CCSS.1.OA.4). Subtraction can be solved by thinking about addition, where instead of taking away, we ask what number added to the subtrahend equals the minuend. For example, to solve 11 - 6, we can think '6 plus what equals 11?' or write it as 6 + ? = 11, and finding the missing addend (5) gives the subtraction answer. This strategy highlights the inverse relationship between addition and subtraction, making it easier for young learners to compute differences by counting on. The problem presents the subtraction 11 - 6 as finding the missing addend in 6 + ? = 11. Choice C is correct because when we add 5 to 6, we get 11, so 6 + 5 = 11, which means 11 - 6 = 5. Choice D is a common error where students add the two numbers instead of finding the difference, resulting in 17, which happens because the connection between addition and subtraction can be abstract for beginners. To help students: Use part-part-whole diagrams showing the relationship; practice on number lines with counting-on (start at 6, count forward to 11); teach fact families explicitly (6+5=11, 5+6=11, 11-6=5, 11-5=6); use 'think addition' language consistently ('to subtract 11-6, think what plus 6 equals 11'); provide many examples connecting subtraction to unknown addend; emphasize that this strategy is especially useful when numbers are close together; use context problems where 'how many more needed' feels natural; practice writing both forms of the problem.
Jamal has 14 cookies. He eats 6 cookies. How many cookies does Jamal have left?
Explanation: This question tests 1st grade ability to solve addition and subtraction word problems within 20 (CCSS.1.OA.1). This is a taking from problem with result unknown. We start with one amount and take away some to find what is left. The story tells us Jamal has 14 cookies and eats 6. Choice A is correct because to find how many cookies Jamal has left, we subtract: 14−6=8. We can represent this as an equation with unknown: 14−6=?. Choice B is a common error where students use the wrong operation, adding instead of subtracting (14+6=20); this happens because choosing the operation from word problem context is challenging. To help students: Act out problems with physical objects; draw pictures representing the situation; teach problem type structures explicitly (adding to, taking from, putting together, taking apart, comparing); use consistent language for each type; practice writing equations with boxes for unknowns; emphasize keywords carefully ('more' can mean add or compare); model thinking aloud ('I started with 14, ate 6, now I need to find what's left, so I subtract'); practice all unknown positions; connect to familiar experiences.
Ava is solving 9+5. She has counting bears and says "I know 9+1=10, so I'll take 1 bear from the 5 bears." What should Ava do next?
Explanation: When you're adding numbers, one smart strategy is to make groups of 10 first, since our number system is based on tens. Ava is using this "make 10" strategy to solve 9+5. Ava correctly identified that 9+1=10, so she took 1 bear from her group of 5 bears. Now she has 10 bears in one group and 4 bears remaining (since 5−1=4). To finish solving 9+5, she needs to add those remaining 4 bears to her group of 10. This gives her 10+4=14, which is the correct answer. Choice A is correct because it completes Ava's strategy properly. Choice B is wrong because counting all the bears from the beginning wastes the smart work Ava already did - she doesn't need to start over. Choice C is wrong because putting the 1 bear back would undo her progress and leave her back where she started with 9+5. Choice D is wrong because Ava's current strategy is working perfectly fine - there's no reason to abandon it when she's almost finished. Remember the "make 10" strategy when adding: if one number is close to 10, borrow from the other number to make 10 first, then add what's left. This makes addition much easier because adding to 10 is simple!
Jake made 4 bundles of ten pencils each. Then he used 6 individual pencils from one bundle for his homework. How many complete bundles of ten does Jake have now?
Explanation: When you see problems about bundles and individual items, you need to carefully track what happens to complete groups when some items are removed. Jake starts with 4 complete bundles of ten pencils each. When he takes 6 individual pencils from one bundle, that bundle is no longer complete - it now has only 4 pencils left (10−6=4). Since a complete bundle must have exactly 10 pencils, this broken bundle doesn't count anymore. This means Jake now has 3 complete bundles of ten pencils, plus one incomplete bundle with 4 pencils. The question asks specifically for complete bundles, so the answer is 3. Let's examine why the other choices are wrong: Choice A (34 complete bundles) makes no sense - Jake never had anywhere near this many bundles to begin with. Choice B (4 complete bundles) is the trap answer. This would be correct if Jake hadn't touched any bundles, but once he removed pencils from one bundle, it's no longer complete. Choice D (10 complete bundles) also makes no mathematical sense given that Jake started with only 4 bundles total. Remember this key strategy: when solving bundle problems, always check whether groups remain "complete" after items are added or removed. The moment you take something out of a complete group, that group is no longer complete, even if other items remain in it.
To add 7+2, start at 7 and count on 2: 8, 9. What number do you end at?
Explanation: This question tests 1st grade ability to relate counting to addition and subtraction (CCSS.1.OA.5). Counting on is an efficient strategy for addition. Instead of counting from 1, start at one of the addends and count forward by the other addend. For example, to solve 8 + 3, start at 8 and count forward 3 numbers: '9, 10, 11'—the last number you say (11) is the answer. The problem asks to add 7 + 2 by counting on from 7. Choice D is correct because starting at 7 and counting on 2 gives '8, 9,' so the answer is 9. Choice C is a common error where students add one extra or miscount by including the starting number; this happens because tracking counts while saying numbers is cognitively demanding. To help students: Model counting on with number lines showing clear starting point and forward jumps; use fingers to track counts while saying numbers aloud; emphasize NOT starting at 1 for counting on; practice with physical objects (start with group, add more by counting on); compare efficiency of counting on vs counting all from 1; practice with small addends (1-5) first; connect counting to written addition equations.
Which symbol makes this true: 4523?
(correct answer)
Explanation: This question tests 1st grade ability to compare two two-digit numbers using place value understanding (CCSS.1.NBT.3). To compare two-digit numbers, always start by comparing the tens place digits. The number with more tens is greater, regardless of the ones; if the tens are equal, then compare the ones place digits—the number with more ones is greater. For example, 45>23 because 4 tens is greater than 2 tens (we don't even need to look at the ones in this case). The stimulus shows two numbers, 45 and 23, that need to be compared with the correct symbol. Choice C is correct because the > symbol accurately shows 45 is greater than 23 since 4 tens > 2 tens. Choice B is a common error where students reverse the comparison symbols, thinking < means greater than, which happens because symbol direction is easily confused like an alligator mouth opening to the bigger number. To help students: Use base-10 blocks to show visual magnitude; emphasize 'compare tens first—that's most important'; practice with number lines showing position; teach symbol direction ('mouth opens to bigger number'); compare numbers with same tens to highlight ones importance; compare numbers with different tens to show tens dominate; provide many examples of 'tricky' cases like 39 vs 41; use place value charts to organize thinking; practice writing comparison statements; connect to real contexts (scores, ages, quantities).
Chen draws a big blue triangle. What makes it a triangle?
Explanation: This question tests 1st grade understanding of defining versus non-defining attributes using a specific example (CCSS.1.G.1). Students must identify which characteristic actually makes a shape a triangle, ignoring non-essential features. The scenario describes Chen's big blue triangle, asking what makes it a triangle. Choice C (It has 3 sides and 3 corners) is correct because these are the defining attributes that make any shape a triangle. Choices A (blue), B (big), and D (position) are all non-defining attributes that don't determine whether something is a triangle. This question helps students focus on essential properties rather than superficial features. To help students: Create triangles of various colors and sizes, asking 'Is this still a triangle? Why?'; sort shapes by type regardless of color or size; use the key phrase 'Count the sides and corners to know the shape!'
Look at 80. How many ones are in 80?
Explanation: This question tests 1st grade understanding that decade numbers (10, 20, 30...90) represent multiples of ten with 0 ones (CCSS.1.NBT.2.c). Decade numbers—10, 20, 30, 40, 50, 60, 70, 80, and 90—are special because they contain only tens and no ones. For example, 80 is 8 tens and 0 ones, which we can see by showing 8 ten-rods with no unit cubes; the digit in the tens place tells us how many tens, and the 0 in the ones place tells us there are no loose ones. The stimulus asks to look at 80 and identify how many ones are in it. Choice C is correct because 80 has exactly 0 ones, following the decade pattern. Choice A is a common error where students think the tens digit is the ones (says 8 ones); this happens because place value is abstract and students reverse tens and ones. To help students: Use base-10 blocks extensively—show only ten-rods with explicit empty space where ones would be; emphasize 0 ones verbally and visually; practice counting by tens (10, 20, 30...90); connect decade numbers to skip counting; compare decades to non-decades (80 vs 88: both have 8 tens, but 88 also has 8 ones); write equations showing 8 tens + 0 ones = 80; use place value charts highlighting the 0 in ones place; have students build each decade with blocks.
The diagram shows rectangles with circles inside them. What should the 4th rectangle look like?
Explanation: The pattern shows rectangles with 2, 4, then 6 circles inside. The pattern adds 2 circles each time, so the 4th rectangle should have 6 + 2 = 8 circles. Choice A (7 circles) adds only 1. Choice C (9 circles) adds 3 instead of 2. Choice D (6 circles) repeats the current rectangle instead of continuing the pattern.
Look at the coins in the picture. Henry picks out all the coins that are worth more than 3 pennies. Which coins does he pick?
Explanation: Coins worth more than 3 cents: nickel (5¢), dime (10¢), and quarter (25¢) are all greater than 3¢. Choice A excludes nickels which are worth 5¢ > 3¢. Choice B excludes quarters. Choice D excludes nickels and dimes which are both worth more than 3¢.
Lisa has 15 marbles. She wants to give away 7 marbles. She decides to first take away 5 marbles, then take away 2 more marbles. Why did Lisa break apart the 7 this way?
Explanation: When you see subtraction problems where someone breaks apart a number, think about what makes subtraction easier. The key is looking for patterns that create simpler math steps. Lisa wants to subtract 7 from 15, but instead of doing 15−7 all at once, she breaks it into 15−5−2. Let's see why this helps. When she first takes away 5 marbles: 15−5=10. Now she has exactly 10 marbles left, which is a nice round number. Then she can easily subtract the remaining 2: 10−2=8. Working with 10 makes the second subtraction much simpler than trying to figure out 15−7 directly. Answer choice A is incorrect because 15−2=13 isn't actually easier to work with than 15 - Lisa didn't subtract 2 first anyway. Answer choice B shows true math (7−5=2) but doesn't explain why breaking apart 7 this particular way makes the problem easier to solve. Answer choice C also shows correct math (5+2=7) but only explains how to check your work, not why this breakdown strategy helps. Answer choice D correctly identifies that 15−5=10 creates a simpler number to work with for the next step. Remember this strategy: when subtracting, look for ways to break apart numbers that will give you "friendly" numbers like 10, 20, or 100 in your intermediate steps. These round numbers make mental math much easier!
Look at the shapes in the picture. Which shape is different from all the others in the most important way?
Explanation: Shape 1 (circle) is the only shape that curves - all others have straight sides and corners. While shapes may differ in size, the most important geometric difference is between curved and straight-sided shapes.
Tom has 10 marbles total in three groups. The first group has 4 marbles. The second group has 1 marble. How many marbles are in the third group?
Explanation: This is a "parts and wholes" problem where you know the total and some of the parts, and need to find the missing part. When you see this type of question, think about how all the pieces add up to make the whole. Let's work through this step by step. Tom has 10 marbles total, split into three groups. You know the first group has 4 marbles and the second group has 1 marble. To find how many marbles are in the third group, you need to subtract the marbles you already know about from the total: 10−4−1=5 marbles in the third group. You can also think of it as: 4+1+?=10. Since 4+1=5, you need 5+?=10, so the missing number is 5. Looking at the wrong answers: Answer A (6 marbles) would give you 4+1+6=11 total marbles, which is too many. Answer B (4 marbles) would give you 4+1+4=9 total marbles, which is one short. Answer D (7 marbles) would give you 4+1+7=12 total marbles, which is way too many. Only answer C gives you exactly 10 marbles: 4+1+5=10. Study tip: For missing part problems, always check your answer by adding all the parts together. They should equal the total you were given in the problem.
Study the picture of shapes. Which statement about these shapes is true?
Explanation: The triangle has 3 corners, the square has 4 corners, and the rectangle has 4 corners. All have at least 3 corners. They don't all have the same number of corners, they don't all have only straight sides (if a circle were included), and they don't all have curved sides.
Subtract the tens: 40−30=.
Explanation: This question tests 1st grade subtraction of multiples of 10 in the range 10-90 (CCSS.1.NBT.6). When subtracting multiples of 10, use place value strategy: subtract tens from tens. Since both numbers end in 0 (have 0 ones), we only work with the tens place. The stimulus directly asks to subtract the tens for 40 - 30. Choice C is correct because 4 tens - 3 tens = 1 ten = 10.ChoiceAisacommonerrorwherestudentsaddinsteadofsubtract,getting40 + 30 = 70,whichhappensbecausesubtractionismorechallengingthanaddition.Tohelpstudents:Usebase−10blockstophysicallyremoveten−rods,countingwhatremains;practiceonnumberlineswithbackwardjumpsof10;emphasize′subtracttensfromtens′strategy;connecttoskipcountingbackwardby10s;providemanyexamplesshowingpattern;useplacevaluechartstoorganizetens;connecttoadditionasinverse(10 + 30 = 40$).
Use the ten frame shown. If 3 more dots are added to fill some empty spaces, how many dots will be in the ten frame?
Explanation: The ten frame shows 7 dots initially. Adding 3 more gives 7+3=10 dots total. Choice B is the original number of dots. Choice C results from adding 7+3+3. Choice D is just the number of empty spaces originally.
Alex counts 16 buttons and sorts them into 1 group of ten and 6 single buttons. He wants to show this to his mom using words and numbers. What should Alex say?
Explanation: When you're working with place value, you need to understand what "tens" and "ones" mean and how they combine to make numbers. Alex has 16 buttons total. He sorted them into 1 group of ten buttons and 6 single buttons. This is exactly what place value is about - breaking numbers into groups of ten and leftover ones. The correct way to describe this is "I have 1 ten and 6 ones which makes 16" - answer C. Here's why: 1 ten equals 10, and 6 ones equals 6. When you add them together: 10+6=16. This matches the total number of buttons Alex counted. Let's see why the other answers don't work. Answer A says "1 ten and 6 ones which makes 7" - this gets the grouping right but adds incorrectly. You can't ignore the ten when counting the total. Answer B says "6 tens and 1 one which makes 61" - this flips the numbers around completely. Alex doesn't have 6 groups of ten buttons. Answer D says "16 tens and 0 ones which makes 160" - this would mean Alex has 16 groups of ten buttons each, which is 160 buttons total, not 16. Remember this pattern: when you see a two-digit number like 16, the first digit (1) tells you how many tens, and the second digit (6) tells you how many ones. Always check that your tens and ones add up to match the original number.
Find 56+10 mentally. Change the tens digit, not the ones.
Explanation: This question tests 1st grade ability to mentally find 10 more or 10 less than a two-digit number (CCSS.1.NBT.5). To add or subtract 10 mentally, use place value understanding: since 10 equals 1 ten and 0 ones, adding 10 means adding 1 ten (so the tens digit increases by 1), while the ones digit stays the same. For example, 34 + 10 = 44 because 3 tens + 1 ten = 4 tens, and the 4 ones remain unchanged. Similarly, subtracting 10 means removing 1 ten (tens digit decreases by 1), while ones stay the same: 67 - 10 = 57 because 6 tens - 1 ten = 5 tens, and the 7 ones remain unchanged. The stimulus asks to find 56 + 10 mentally by changing the tens digit, not the ones. Choice C is correct because adding 10 to 56 means adding 1 ten: 5 tens + 1 ten = 6 tens, ones stay 6, giving 66. Choice A is a common error where students add 1 instead of 10, changing the ones digit to 7; this happens because understanding 10 as 1 ten is abstract and students sometimes focus on the digit '10' rather than its place value meaning. To help students: Use base-10 blocks to show physically adding/removing 1 ten-rod while ones stay constant; practice on hundred charts (add 10 = down one row, subtract 10 = up one row); emphasize pattern 'tens change by 1, ones stay same'; provide many examples showing ones digit constant; connect to skip counting by 10s; use number lines with jumps of 10; practice mental math daily with quick '10 more/less' questions; explain why this is efficient compared to counting by ones; make the place value connection explicit.
Maya has 56 stickers. Chen has 52 stickers. Who has more?
Explanation: This question tests 1st grade ability to compare two two-digit numbers using place value understanding (CCSS.1.NBT.3). To compare two-digit numbers, always start by comparing the tens place digits. The number with more tens is greater, regardless of the ones; if the tens are equal, then compare the ones place digits—the number with more ones is greater. For example, 56 > 52 because when tens are equal (both have 5 tens), 6 ones > 2 ones. The stimulus shows a comparison of quantities: Maya with 56 stickers and Chen with 52 stickers, asking who has more. Choice A is correct because Maya has more since when tens are equal (both 5 tens), 6 ones > 2 ones. Choice B is a common error where students only compare ones digits and ignore tens (saying Chen has more because 2 > nothing specific, but miscounting), which happens because place value understanding is still developing. To help students: Use base-10 blocks to show visual magnitude; emphasize 'compare tens first—that's most important'; practice with number lines showing position; teach symbol direction ('mouth opens to bigger number'); compare numbers with same tens to highlight ones importance; compare numbers with different tens to show tens dominate; provide many examples of 'tricky' cases like 39 vs 41; use place value charts to organize thinking; practice writing comparison statements; connect to real contexts (scores, ages, quantities).
At a farm, there were 8 chickens in the yard. The farmer brought 5 more chickens from the barn. Later, 3 chickens went into the barn to rest. Which equation shows the total number of chickens that were in the yard after the farmer brought more from the barn?
Explanation: The question asks for the total after the farmer brought 5 more chickens from the barn, which is 8 + 5 = 13. This is before the 3 chickens went to rest. Choice B shows what happened after 3 went to rest. Choice C includes both events. Choice D shows operations in wrong order.
Based on the picture, Emma groups the coins by their value. She puts coins of the same value together. How many different groups does she make?
Explanation: The picture shows quarters (25¢), dimes (10¢), and nickels (5¢) - that's 3 different values, so 3 groups. Choice A undercounts the coin types. Choice C would be correct if pennies were also shown. Choice D counts too many groups.
Three friends are comparing their baseball bats. Alex's bat is longer than Jamie's bat. Chris's bat is shorter than Jamie's bat. If they want to line up their bats from shortest to longest, which friend's bat goes first?
Explanation: This tests ordering three objects where the relationships create a chain: Alex > Jamie > Chris, so Chris is shortest. Choice C correctly identifies that the shortest goes first in a shortest-to-longest arrangement. Choice A uses irrelevant alphabetical information. Choice B misunderstands that being mentioned frequently doesn't indicate position in length order. Choice D ignores the given length relationships.
Complete the subtract-to-10 step: 15−7=15−5− .
Explanation: This question tests 1st grade fluency in addition and subtraction within 20, with emphasis on strategies (CCSS.1.OA.6). For subtraction across 10, decompose the subtrahend to first reach 10, then subtract the rest. For 13 - 4, we think: 13 to 10 is 3, so break 4 into 3 + 1. Then: 13 - 4 = (13 - 3) - 1 = 10 - 1 = 9. The problem asks to complete the subtract-to-10 step for 15 - 7 = 15 - 5 - _. Choice B is correct because to get to 10 from 15 is subtracting 5, and the remaining part of 7 is 2 (since 7 = 5 + 2). Choice A is a common error where students confuse which number to decompose, such as thinking it's 1 instead; this happens because decomposing numbers flexibly is challenging. To help students: For decomposing to 10 in subtraction, practice with many examples showing the 'get to 10 first' step; use ten-frames; provide daily practice with mixed strategies; emphasize that facts within 10 should be automatic.
Find the missing number: 9−4=.
Explanation: This question tests 1st grade ability to determine the unknown whole number in an addition or subtraction equation (CCSS.1.OA.8). When the unknown is the result in a subtraction equation (like in a - b = ?), we simply subtract the subtrahend from the minuend to find the difference. We can use counting back, objects, or number lines to compute it directly. The equation is 9 - 4 = __. Choice D is correct because 9 - 4 = 5, so the unknown is 5. Choice A is a common error where students add the numbers instead of subtracting, getting 9 + 4 = 13; this happens because they may misread the operation or not recognize the need for the inverse. To help students: Teach each unknown position explicitly (result, subtrahend, minuend); show how to check answer by substituting back into equation; for result unknown in subtraction, it's direct computation; use part-part-whole diagrams to visualize relationships; practice with concrete examples using objects; show related fact families (if 9-4=5, then 5+4=9); emphasize checking: substitute answer back into equation to verify it's true.